Question:
Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
Correct Answer
$10830
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5700 × 10% × 9
= $5700 ×10/100 × 9
= 5700 × 10 × 9/100
= 57000 × 9/100
= 513000/100
= $5130
Thus, Simple Interest = $5130
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $5130
= $10830
Thus, Amount to be paid = $10830 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5700
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5700 + ($5700 × 10% × 9)
= $5700 + ($5700 ×10/100 × 9)
= $5700 + (5700 × 10 × 9/100)
= $5700 + (57000 × 9/100)
= $5700 + (513000/100)
= $5700 + $5130 = $10830
Thus, Amount (A) to be paid = $10830 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5700, the simple interest in 1 year
= 10/100 × 5700
= 10 × 5700/100
= 57000/100 = $570
Thus, simple interest for 1 year = $570
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $570 × 9 = $5130
Thus, Simple Interest (SI) = $5130
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $5130
= $10830
Thus, Amount to be paid = $10830 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?
(3) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(5) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?
(7) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.